FoCM 2014 conference
Workshop A1 - Computational Dynamics
December 11, 17:00 ~ 17:25 - Room B21
Coexistence of hexagons and rolls
Jean-Philippe Lessard
Université Laval, Canada - jean-philippe.lessard@mat.ulaval.ca
In this talk we introduce a rigorous computational method for finding heteroclinic solutions of a system of two second order differential equations. These solutions correspond to standing waves between rolls and hexagonal patterns of a two-dimensional pattern formation PDE model. After reformulating the problem as a projected boundary value problem (BVP) with boundaries in the stable/unstable manifolds, we compute the local manifolds using the Parameterization Method and solve the BVP using Chebyshev series and the radii polynomial approach. Our results settle a conjecture by Doelman et al. about the coexistence of hexagons and rolls.
Joint work with Jan Bouwe van den Berg (VU Amsterdam), Andréa Deschênes (Laval) and Jason Mireles James (Rutgers).